German Patent Application No. 42 13 792 describes a method for operating a data transmission system where data is transmitted to several other stations using a call message, referred to as Call Offering Procedure (COP), sent by a station having the bus access right. The other stations, which have been requested by the COP to transmit a response message, send their response messages in a predefined sequence in time slots of fixed length over the bus line. The options for defining this sequence include hardware coding by the user at startup, parameterization in the initializing phase, or a definition as a function of the station addresses. Direct mapping of station addresses to time slot numbers should be mentioned as a variant that can be implemented inexpensively, where the time slot starting with time t1 is assigned to the station having address 1, time slot at t2 to address 2, etc. The known method improves the transmission rate, but does not represent an optimum solution.